🚀 go-pugleaf

In article <367@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes:
>In article <1992Nov20.140159.4770@sun0.urz.uni-heidelberg.de>, gsmith@l
auren.iwr.uni-heidelberg.de (Gene W. Smith) writes:
>> "Uncountable" means no one-to-one relation with the integers
>> can be given.  This does not refer to a formal system.
>
>Unless you have a formal system in which to determine what constitutes
>a one-to-one relationship you are not doing mathematics.

If this is so Mr. Budnik, then what do you call the activities of all
those people in math departments all over the world who don't even know
the STATEMENT of the Lowenheim-Skolem theorem?  I.e., probably most
working mathematicians who are not logicians?  You may call it
"philosophy", but the rest of the world calls it "mathematics".  The
people that do this "mathematics" which you insist is "philosophy"
don't look at formal systems to tell them what constitutes a one-one
relationship.  You can say that they're operating without foundations
(they'd probably be glad to agree!), or you can say they're just a
bunch of Platonists, but it is an abuse of language to insist that
they're doing "philosophy".
-- 
Ian Sutherland
ian@eecs.nwu.edu

Sans Peur